Preflop I like calling to the 3bet.
We have a hand with quite good play ability, also we are given very good odds.
The only thing that really sucks is that we are OOP.
The factors that we should be aware of in my opinion are:
- our hand - for example I'm folding 87o here
- villain's image - if we know something about him we can adjust our play better. If he's unknown I'd be tighter.
- the effective stack - this is very important. If villain have 20bb stack, then there is no point in calling, but if he has like 80bb then calling gets better because we have more implied odds.

I don't really like check/calling the flop.
So, we have two overcards, and some backdoors as well, but I don't really think it is good enough to call.
The biggest problem is that we are easily dominated (for example he has quite a lot of AQ/AJ/KQ/KJ hands probably), also we can't really call a bet on the turn with Q high.
I just prefer folding here.

[quote]What is the thought process for putting him onto a range?[quote]

Well, basically it is hard to put him on a range in this situation because he is unknown, also his preflop action was very weird, so it could vary from KK+ only to a lot of junk hands, like 85o.
In general, I'd put him on some big pair, good broadways and also I'd add him some crap hands like J7s as well.

As played on the flop, check/calling turn is fine.
The card boosts a lot our equity, but I see no point in raising here because if we stack of we will never be ahead.